What is 1+tan^2(90-x) ?

The solution to 1+tan^2(90-x) is csc^2(x)

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simplify 1+tan^2(90-x)

simplify

1 + tan^{2} (9 0^{\circ} - x)

csc^{2} (x)

Solution steps

1 + tan^{2} (9 0^{\circ} - x)

Rewrite using trig identities

= 1 + (\frac{cos ( x )}{sin ( x )})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= 1 + \frac{cos ^{2} ( x )}{sin ^{2} ( x )}

Rewrite using trig identities

= csc^{2} (x)

tan (\frac{π}{3} + x)

csc (arcsin (u))

sin (2 x) - sin (- 2 x)

42 cos (π x - \frac{π}{4})

4 sin (\frac{x}{3} - \frac{π}{3})